Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-8x-7y &= 2 \\ 8x+6y &= -2\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $8x = -6y-2$ Divide both sides by $8$ to isolate $x$ $x = {-\dfrac{3}{4}y - \dfrac{1}{4}}$ Substitute this expression for $x$ in the first equation. $-8({-\dfrac{3}{4}y - \dfrac{1}{4}}) - 7y = 2$ $6y + 2 - 7y = 2$ Simplify by combining terms, then solve for $y$ $-1y + 2 = 2$ $-1y = 0$ $y = 0$ Substitute $0$ for $y$ in the top equation. $-8x-7( 0) = 2$ $-8x = 2$ $-8x = 2$ $x = -\dfrac{1}{4}$ The solution is $\enspace x = -\dfrac{1}{4}, \enspace y = 0$.